Rare-event component importance for the consecutive-k system

Various indices of component importance with respect to system reliability have been proposed. The most popular one is the Birnbaum importance. In particular, a special case called uniform Birnbaum importance in which all components have the same reliability p has been widely studied for the consecutive-k system. Since it is not easy to compare uniform Birnbaum importance, the literature has looked into the case p = 1/2, p --> 1, or p greater than or equal to 1/2. In this paper, we look into the case p --> 0 to complete the spectrum of examining Birnbaum importance over the whole range of p. (C) 2002 Wiley Periodicals, Inc.